160 REPORT— 1892. 



mean of that and c. It was found, however, that A and B always read 

 almost exactly alike, and c was not usually more than one or two tenths 

 of a degree lower. In any future instrument it would douhtless be 

 sufl&cient to determine the temperature of the copper case by a single 

 thermometer sunk in one of the side faces, midway between the front and 

 back face. 



In spite of the felt packing the temperature of the case was found to 

 change more rapidly when the instrament was exposed to the sun than 

 was to be desired, and Professor McLeod found it an improvement to 

 introduce a screen of tinned iron placed a little distance in front of the 

 front side of the cube, and of course provided with a hole for letting the 

 sun's rays through that were to fall upon the thermometer D. In most 

 of the observations the case thermometers were mei'ely sunk in their 

 holes, the sides of which the bulbs might or might not touch in one or 

 two places. It was feared that in spite of the slowness of the change of 

 temperature of the case, the lagging of the case thermometers might 

 possibly introduce a sensible eri'or. Accordingly the effect was tried of 

 introducing a packing of reduced silver between the bulb of the thermo- 

 meter and the wall of the cavity in which it was inserted. By packing 

 in this manner one of the thermometers A, B, and leaving the other 

 unpacked, it was possible to judge whether any sensible error was to be 

 apprehended from lagging. It was found that the packed thermometer 

 was a little more prompt, but the difference of temperatures read oS was 

 very small, little more than emerging from errors of observation. 



In the first regular observation on the march of the thermometers 

 under insolation, the four thermometers were read before exposure, then 

 the instrument was exposed, and the thermometers read at intervals of a 

 minute for a quarter of an hour, by which time thermometer D had 

 become sensibly stationary, having risen 61°'3, while the case thermo- 

 meters rose about 2°, the excess of D over the temperature of the case 

 rising to 49°7. The sun was then screened off, and the reading of all 

 the thermometers at intervals of one minute continued for about half an 

 hour. During this time the case thermometers continued slowly to rise, 

 the total rise in the half-hour amounting to 1°"5 ; the central thermometer 

 fell, pretty rapidly towards the beginning, slowly near the end, till it 

 stood only 0°'4 or 0°'5 above the case thermometers. The sky was very 

 clear, and there were no clouds near the sun ; and as the insolation began 

 at XII., 26, the decrease of the sun's altitude during insolation was but 

 small. 



It remains to be shown whether, and if so in what way, a measure of 

 the radiation can be obtained from the results. 



Let be the tempei^ature of the insolated thermometer, T that of the 

 case as measured by the case th'ermometers, q the coefficient of cooling, 

 the rate of cooling being taken as following Newton's law, r the rate of 

 heating of D due to solar radiation. Then in the time dt the increment 

 dO of d's temperature is made up of the gain, rdt, due to radiation and 

 the loss, q(6 — t), due partly to convection, partly to the excess of the 

 radiation from D to the case over that from the case to D. We have 

 therefore ^^ 



|^ + 2(^-T)=r (n 



If we suppose r and t constant, or subject only to slow secular changes, 

 so that they may be deemed constant in the integration, we have 



